Kingman's model with random mutation probabilities: convergence and condensation II

Yuan, Linglong ORCID: 0000-0002-7851-1631 (2020) Kingman's model with random mutation probabilities: convergence and condensation II. Journal of Statistical Physics, 181 (3). pp. 870-896.

This is the latest version of this item.

Access the full-text of this item by clicking on the Open Access link.

Text
official publication.pdf - Published version
Available under License : See the attached licence file.
Download (478kB)

Official URL: https://link.springer.com/article/10.1007%2Fs10955...

Abstract

A generalisation of Kingman’s model of selection and mutation has been made in a previous paper which assumes all mutation probabilities to be i.i.d.. The weak convergence of fitness distributions to a globally stable equilibrium was proved. The condensation occurs if almost surely a positive proportion of the population travels to and condensates on the largest fitness value due to the dominance of selection over mutation. A criterion of condensation was given which relies on the equilibrium whose explicit expression is however unknown. This paper tackles these problems based on the discovery of a matrix representation of the random model. An explicit expression of the equilibrium is obtained and the key quantity in the condensation criterion can be estimated. Moreover we examine how the design of randomness in Kingman’s model affects the fitness level of the equilibrium by comparisons between different models. The discovered facts are conjectured to hold in other more sophisticated models.

Item Type:	Article
Uncontrolled Keywords:	Population dynamics, Mutation-selection balance, House of cards, Random matrices, Size-biased distribution, Bose-Einstein condensation
Depositing User:	Symplectic Admin
Date Deposited:	18 Sep 2020 07:20
Last Modified:	18 Jan 2023 23:37
DOI:	10.1007/s10955-020-02609-w
Open Access URL:	https://link.springer.com/article/10.1007%2Fs10955...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3097299